幂的运算法则（讲义）课前预习1.背默乘方的相关概念：求n个相同因数a的积的运算叫做乘方，乘方的结果叫做___．用字母表示为na，其中______叫底数，______叫指数，读作“________________”．2.补全表格：底数指数读作3232525()mab3.类比迁移：老师出了一道题，让学生计算45aa．小明是这么做的：4545459aaaaaaaaaaaaa个个请你类比小明的做法计算：mnaa．知识点睛幂的运算法则：1.同底数幂相乘，_________，_________．即_____________．2.同底数幂相除，_________，_________．即_____________．3.幂的乘方，___________，___________．即_____________．4.积的乘方等于___________．即_____________．规定：0a_______（___________）；pa______=______（_________________________）．精讲精练1.①122mm________；②31·maa________；③2·mnnpp________；④2121()()nnabab______；⑤mnmnaaa________；⑥124mmmxxxx______；⑦23273n_________；⑧432()()aaa_________．2.①21mmaa__________；②233mm_____________；③63(2)(2)_______；④82()()mnmn______；⑤3622____________；⑥20152016333_________；⑦221222mmm⑧3212mmmpppp=______________=_______________=______________=_______________⑨2242(2)2；⑩220211(π7)332．3.①23(5)__________；②32()a______________；③42()nb____________；④2()mxx_____________；⑤43()()nnbb_______；⑥26435()()aa____________；⑦()()mnnmpp_________；（p≠0）⑧322326()()()nnnbbb___________．（b≠0）4.①3(2)x____________；②43()ab______________；③22()na__________；④6()nxy_____________．⑤3322(3)(2)xx⑥1001001001236=_______________=_______________=_______________=_______________=_______________=_______________5.①2(3)a______________；②24()ab_____________；③22()nxy__________．④242(2)(2)xx⑤20152016201513412=_______________=_______________=_______________=_______________=_______________=_______________=_______________6.下列运算正确的是_________．（填写序号）①336()aa；②236(2)8aa；③22mmbbb；④mmaaa；⑤31(2)8；⑥4442bbb．7.（1）若32110nnaaa，则n________；（2）若22()nnxxx，则n_________；（3）若3039273mmm，则m______；（4）若212128x，则x________；（5）若105x，则210x________；（6）若105x，102y，则10xy________；（7）若2na，3nb，则6n________．8.混合运算：①2(21)(12)(21)mmxxx（m为正整数）；②5324102()(2)()xxxxx；③1032132(3)4；④1021(3.14)(2)(1)3．【参考答案】课前预习1.幂，a，n，a的n次幂2.2，3，2的3次幂2，3，2的3次幂的相反数25-，5，25-的5次幂(a+b)，(a+b)的m次幂3.mna知识点睛1.底数不变，指数相加，am·an=am+n2.底数不变，指数相减，am÷an=am-n3.底数不变，指数相乘，()mna=amn4.乘方的积，(ab)n=anbn规定：1（a≠0）；1pa1()pa（a≠0，p是正整数）精讲精练1.①22m+1②a3m③-p2m④(a+b)4n⑤a2m⑥-3x2m+1⑦32n⑧-a92.①am+1②-m③-8④-(m+n)6⑤8⑥1⑦2⑧0⑨-1⑩2743.①②-a6③b8n④x2m+1⑤b-n⑥4a12⑦1⑧14.①8x3②a3b12③an④-xny6n⑤-55x6⑥15.①9a2②a8b4③-x2ny4n④0⑤-36.②7.（1）4；（2）2；（3）5；（4）3；（5）25；（6）10；（7）ab8.①(2x-1)3m+1；②14x8；③478；④74
